Hyers-Ulam stability of linear differential equations of first order

Abstract

We prove the Hyers-Ulam stability of linear differential equations of first order, ~(t)y' (t) = y(t).Indeed, this paper deals with a generalization of a paper by Alsina and Ger [1] or of papers by Miura, Takahasi and Choda [2] and by Miura [3]. (~)

Hyers-Ulam stability of fractional linear differential equations involving Caputo fractional derivatives

“…In recent years, many researchers have focused on the study of Hyers-Ulam stability of differential equations, and gained a series of results (see [1]- [7] and [9]- [14] and the references therein).…”

An integrating factor approach to the Hyers-Ulam stability of a class of exact differential equations of second order

“…Soon afterwards, such stability results of the differential equation y = λy in various abstract spaces have been obtained by Miura and Takahasi et al [12,13,22]. Since then, many interesting results on the Ulam stability of different types of differential equations have been established by various authors [1,3,4,5,7,8,9,10,11,14,15,17,18,19,20,21,23].…”

Note on the stability of first order linear differential equations

“…Jung [4][5][6][7] applied the fixed point method for proving the Hyers-Ulam-Rassias stability of a Volterra integral equation of the second kind and for differential equations of first order. Using the same technique we prove the Hyers-Ulam-Rassias stability and Hyers-Ulam stability of differential equation…”